Research PapersNo Access

FRACTIONAL QUANTUM HALL STATES WITH NEGATIVE FLUX: EDGE MODES IN SOME ABELIAN AND NON-ABELIAN CASES

M. V. MILOVANOVIĆ

Institute of Physics, P. O. Box 68, 11080 Belgrade, Serbia

Search for more papers by this author

and

TH. JOLICOEUR

Laboratoire de Physique Théorique et Modèles Statistiques, Universitè Paris-Sud, 91405 Orsay, France

Search for more papers by this author

https://doi.org/10.1142/S0217979210055081Cited by:7 (Source: Crossref)

Abstract

We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general, quantum Hall states have many edge states. Here, we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction ν = 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor ν = 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally, we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve, in all cases, explicit derivative operators diminishing the angular momentum of the system.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983), DOI: 10.1103/PhysRevLett.50.1395. Web of Science, ADS, Google Scholar
J. K. Jain, Phys. Rev. Lett. 63, 199 (1989), DOI: 10.1103/PhysRevLett.63.199. Web of Science, ADS, Google Scholar
S. Das Sarma and A. Pinczuk (eds.) , Perspectives in Quantum Hall Effect ( Wiley , New York , 1996 ) . Google Scholar
O. Heinonen (ed.) , Composite Fermions: A Unified View of the Quantum Hall Regime ( World Scientific , Singapore , 1998 ) . Google Scholar
J. K. Jain , Composite Fermions ( Cambridge University Press , Cambridge , 2007 ) . Google Scholar
G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991), DOI: 10.1016/0550-3213(91)90407-O. Web of Science, ADS, Google Scholar
N. Read and G. Moore, Prog. Theor. Phys. (Kyoto) Suppl. 107, 157 (1992), DOI: 10.1143/PTPS.107.157. ADS, Google Scholar
W. Panet al., Phys. Rev. Lett. 90, 016801 (2003), DOI: 10.1103/PhysRevLett.90.016801. Web of Science, Google Scholar
J. S. Xiaet al., Phys. Rev. Lett. 93, 176809 (2004), DOI: 10.1103/PhysRevLett.93.176809. Web of Science, ADS, Google Scholar
N. Read and E. H. Rezayi, Phys. Rev. B 54, 16864 (1996), DOI: 10.1103/PhysRevB.54.16864. Web of Science, ADS, Google Scholar
N. Read and E. H. Rezayi, Phys. Rev. B 59, 8084 (1999), DOI: 10.1103/PhysRevB.59.8084. Web of Science, ADS, Google Scholar
Th. Jolicoeur, Phys. Rev. Lett. 99, 036805 (2007), DOI: 10.1103/PhysRevLett.99.036805. Web of Science, Google Scholar
Th. Jolicoeur, Talk given at les Houches summer school "Exact Methods in Low-dimensional Statistical Physics and Quantum Computing", e-print , arXiv:0907.1538 . Google Scholar
G. Möller and S. Simon, Phys. Rev. B 72, 045344 (2005), DOI: 10.1103/PhysRevB.72.045344. Web of Science, Google Scholar
B. I. Halperin, Helv. Phys. Acta 56, 75 (1983). Google Scholar
J. P. Eisensteinet al., Phys. Rev. B 41, 7910 (1990), DOI: 10.1103/PhysRevB.41.7910. Web of Science, ADS, Google Scholar
L. W. Engelet al., Phys. Rev. B 45, 3418 (1992), DOI: 10.1103/PhysRevB.45.3418. Web of Science, ADS, Google Scholar
X. C. Xie, Y. Guo and F. C. Zhang, Phys. Rev. B 40, 3487 (1989), DOI: 10.1103/PhysRevB.40.3487. Web of Science, ADS, Google Scholar
X. G. Wu, G. Dev and J. K. Jain, Phys. Rev. Lett. 71, 153 (1993), DOI: 10.1103/PhysRevLett.71.153. Web of Science, ADS, Google Scholar
X.-G. Wen, Int. J. Mod. Phys. B 6, 1711 (1992), DOI: 10.1142/S0217979292000840. Link, Web of Science, ADS, Google Scholar
A. Balatsky and M. Stone, Phys. Rev. B 43, 8038 (1991), DOI: 10.1103/PhysRevB.43.8038. Web of Science, ADS, Google Scholar
F. D. M. Haldane , The Quantum Hall Effect , 2nd edn. , eds. R. E. Prange and S. M. Girvin ( Springer-Verlag , New York , 1990 ) . Google Scholar
N. Read, Phys. Rev. Lett. 65, 1502 (1990), DOI: 10.1103/PhysRevLett.65.1502. Web of Science, ADS, Google Scholar
A. H. MacDonald, Phys. Rev. Lett. 64, 220 (1990), DOI: 10.1103/PhysRevLett.64.220. Web of Science, ADS, Google Scholar
M. D. Johnson and A. H. MacDonald, Phys. Rev. Lett. 67, 2060 (1991), DOI: 10.1103/PhysRevLett.67.2060. Web of Science, Google Scholar
F. D. M. Haldane, Phys. Rev. Lett. 74, 2090 (1995), DOI: 10.1103/PhysRevLett.74.2090. Web of Science, Google Scholar
C. L. Kane, M. P. A. Fisher and J. Polchinski, Phys. Rev. Lett. 72, 4129 (1994), DOI: 10.1103/PhysRevLett.72.4129. Web of Science, ADS, Google Scholar
C. L. Kane and M. P. A. Fisher, Phys. Rev. B 52, 17393 (1995), DOI: 10.1103/PhysRevB.52.17393. Web of Science, ADS, Google Scholar
A. M. Chang, L. N. Pfeiffer and K. W. West, Phys. Rev. Lett. 77, 2538 (1996), DOI: 10.1103/PhysRevLett.77.2538. Web of Science, ADS, Google Scholar
U. Zülicke, A. H. MacDonald and M. D. Johnson, Phys. Rev. B 58, 13778 (1998), DOI: 10.1103/PhysRevB.58.13778. Web of Science, ADS, Google Scholar
E. V. Deviatovet al., J. Exp. Theor. Phys. Lett. 82, 539 (2005). Web of Science, Google Scholar
Z.-X. Huet al., Phys. Rev. B 78, 235315 (2008), DOI: 10.1103/PhysRevB.78.235315. Web of Science, ADS, Google Scholar
G. S. Jeon and J. K. Jain, Phys. Rev. B 68, 165346 (2003), DOI: 10.1103/PhysRevB.68.165346. Web of Science, ADS, Google Scholar
A. Cappeli, L. S. Georgiev and I. T. Todorov, Nucl. Phys. B 599, 499 (2001), DOI: 10.1016/S0550-3213(00)00774-4. Web of Science, ADS, Google Scholar
M. Milovanović and N. Read, Phys. Rev. B 53, 13559 (1996), DOI: 10.1103/PhysRevB.53.13559. Web of Science, ADS, Google Scholar